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It is demonstrated that the bandwidth of circular polarization (CP) can be significantly increased when one more parasitic loop is added inside the original loop. A single-loop antenna has only one minimum axial ratio (AR) point while the two-loop antenna can create two minimum AR points. An appropriate combination of the two minimum AR points results in a significant enhancement for the CP bandwidth. A comprehensive study of the new type of broad-band circularly polarized antennas is presented. Several loop configurations, including a circular loop, a rhombic loop, and a dual rhombic loop with a series feed and a parallel feed, are investigated. The AR (≤2 dB) bandwidth of the circular-loop antenna with a parasitic circular loop is found to be 20%, more than three times the AR bandwidth of a single loop. For the rhombic-loop antenna with a parasitic rhombic loop, an AR bandwidth (AR≤2dB) of more than 40% can be achieved by changing the rhombus vertex angle. The AR (≤2 dB) bandwidths of the series-fed and parallel-fed dual rhombic-loop antennas with a parasitic element are 30% and 50%, respectively. A broad-band balun is incorporated into the series-fed dual rhombic-loop antenna for impedance matching. The broad-band CP performance of the loop antennas is verified by experimental results.